**Hypothesis Testing Example****Objective:** Test the following claim (\( H_a \)) at a significance level of \( \alpha = 0.10 \).**Null Hypothesis (\( H_0 \)):** \( \mu = 55.4 \)**Alternative Hypothesis (\( H_a \)):** \( \mu < 55.4 \)**Sample Information:** You assume the population is normally distributed but the standard deviation is unknown. You collect the following sample data:- 19.2- 19.2- 76- 41**Questions:**1. **What is the test statistic for this sample?** - Provide the test statistic accurate to three decimal places.2. **What is the p-value for this sample?** - Provide the p-value accurate to four decimal places.**Decision Criteria:**- Determine if the p-value is: - Less than (or equal to) \( \alpha \) - Greater than \( \alpha \)**Conclusion:**Based on the test statistic, make a decision to either:- Reject the null hypothesis- Accept the null hypothesis- Fail to reject the null hypothesis As such, the final conclusion is that...- There is sufficient evidence to warrant rejection of the claim that the population mean is less than 55.4.- There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 55.4.- The sample data support the claim that the population mean is less than 55.4.- There is not sufficient sample evidence to support the claim that the population mean is less than 55.4.

Given that: Data points [19.2, 19.2, 76.0, 41.0] From Data points we get following: x̄= 38.85 ,s=…

Answered: You wish to test the following claim…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

The following data was collected during the Framingham Heart Study. Is there a statistically significant difference in mean SBP between men and women using a 5% level of significance? Sample size Mean Standard Deviation Men 1623 128.2 17.5 Women 1911 126.5 20.1
Refer to the data set in the accompanying table. Assume that the paired sample data is a simple random sample and the differences have a distribution that is approximately normal. Use a significance level of 0.05 to test for a difference between the weights of discarded paper (in pounds) and weights of discarded plastic (in pounds). In this example, Hd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the weight of discarded paper minus the weight of discarded plastic for a household. What are the null and alternative hypotheses for the hypothesis test? OA. Ho: Hd #0 H₁: Hd>0 O C. Ho: Hd #0 H₁: Hd=0 Identify the test statistic. t= (Round to two decimal places as needed.) B. Ho: Hd=0 H₁: Hd #0 O D. Ho: Hd = 0 H₁: Hd <0 More Info Household Paper 16.39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 POTBRANN~~~~~~~ 7.57 11.42 6.44 20.12 2.41 6.05 2.80 13.61 13.05 17.65 8.72 6.16 7.72 7.98 6.38 6.67 6.98 29 11.08 5.86…
In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales, 10 rock specimens were weighed in grams on each scale. The following data presented in the table were obtained. Can you conclude that the mean weight differs between the scales? Use a=0.03. Specimen Weight on Scale 1 Weight on Scale 2 d; 1 11.23 11.27 -0.04 2 14.36 14.41 -0.05 3 8.33 8.35 -0.02 4. 10.50 10.52 -0.02 23.42 23.41 0.01 6 9.15 9.17 -0.02 7 13.47 13.52 -0.05 8 6.47 6.46 0.01 9 12.40 12.45 -0.05 10 19.38 19.35 0.03 What are the critical values? A. -1.833,1.833 B. -2.574,2.574 C. -2.398,2.398 D. -2.262,2.262 What is the test statistic and conclusion? A. -2.204; Reject Ho B. -2.204; Fail to reject Ho C. -2.108; Reject Ho D. -2.108; Fail to reject Ho
The following data set are four replicas for the measurements of the concentration in Molarity of NaCl in Human Serum (0.161, 0.163, 0.165, and 0.169) calculate: The arithmetic mean or sample mean The Median The sample standard deviation The range or spread Conduct the t-student’s test with 95% confidence
For the following dataset, you are interested to determine the "spread" of the data. Would you employ calculations for the sample standard deviation, or population standard deviation for this dataset: The weight of each apple in a shipment of 1000 apples.
Consider the following data: x 4 5 6 7 8 P(X = x) 0.2 0.2 0.1 0.2 0.3 Step 3 of 5: Find the standard deviation. Round your answer to one decimal place. Copy Data
The weight gains of animals during a period of confinement follow a normal distribution of mean 39.0 and standard deviation 1.0 kg. Answer the following questions.a. Above what weight gain are 99% of the animals?
Consider the data from the Anthropology 105 class. The mean for women is 64.33 in and the standard deviation is 2.64 in. The average height of men in the US is approximately 5ft 10in. What proportion of women represented here are shorter than the average man?
Assuming that the heights of college women are normally distributed with mean 63 inches and standard deviation 1.7 inches, answer the following questions. (Hint: Use the figure below with mean u and standard deviation O.) Area Under a Normal Curve 2.35% 13.5% 34% 34% 13.5% 2.35% P- 30 u - 20 u + 20 u + 30 68% 95% 99.7% (a) What percentage of women are taller than 63 inches? % (b) What percentage of women are shorter than 63 inches? (c) What percentage of women are between 61.3 inches and 64.7 inches? (d) What percentage of women are between 59.6 and 66.4 inches?
What is the standart- deviation of Y in the following data? Select one: 34/6 34 none 34/6
For a population with mean 90 and standard deviation 10 A. find the percentile rank for a score of 95 B. Find the cutoff score (for the population with mean 90, not the z score) for top 2% C. Find the cutoff score (for the population with mean 90, not the z score) for the lowest 20 %

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

You wish to test the following claim (Ha) at a significance level of a = 0.10. H.:µ = 55.4 Ha:µ < 55.4 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 19.2 19.2 76 41